We survey general techniques and open problems in numerical linear algebra on parallel architectures. We first discuss basic principles of parallel processing, describing the costs of basic operations on parallel machines, including general principles for constructing efficient algorithms. We

and time consuming process. The work described here can help in automating much of this process. We will concentrate our e orts on the widely used linear algebra kernels called the Basic Linear Algebra Subroutines (BLAS). In particular, the work presented here is for general matrix multiply, DGEMM. However

This paper describes an extension to the set of Basic Linear Algebra Subprograms. The extensions are targeted at matrix-vector operations which should provide for efficient and portable implementations of algorithms for high performance computers.

Currently, most approaches to retrieving textual materials from scientific databases depend on a lexical match between words in users' requests and those in or assigned to documents in a database. Because of the tremendous diversity in the words people use to describe the same document, lexical methods are necessarily incomplete and imprecise. Using the singular value decomposition (SVD), one can take advantage of the implicit higher-order structure in the association of terms with documents by determining the SVD of large sparse term by document matrices. Terms and documents represented by 200-300 of the largest singular vectors are then matched against user queries. We call this retrieval method Latent Semantic Indexing (LSI) because the subspace represents important associative relationships between terms and documents that are not evident in individual documents. LSI is a completely automatic yet intelligent indexing method, widely applicable, and a promising way to improve users...

• Linear algebra review • A complete reconstruction pipeline • Geometric preliminaries • Tools and libraries • Other techniques • Factorization methods • Motion estimation with RGBD

for the implementation of linear algebra operators on programmable graphics processors (GPUs), thus providing the building blocks for the design of more complex numerical algorithms. In particular, we propose a stream model for arithmetic operations on vectors and matrices that exploits the intrinsic parallelism

this technical convenience. However, the most important result of this book is that the two senses coincide; we will prove that in the section after this one

We present performance results for dense linear algebra using recent NVIDIA GPUs. Our matrix-matrix multiply routine (GEMM) runs up to 60 % faster than the vendor’s implementation and approaches the peak of hardware capabilities. Our LU, QR and Cholesky factorizations achieve up to 80

This is a special topics in linear algebra course taught in the summer of

Linear algebra represents, with calculus, the two main mathematical subjects taught in science universities. However this teaching has always been difficult. In the last two decades, it became an active area for research works in mathematics education in several countries. Our goal is to give a